Research Article
Year 2022,
Volume: 71 Issue: 3, 710 - 719, 30.09.2022
Abstract
References
- Adamowicz, T., Harjulehto, P., Hastö, P., Maximal operator in variable exponent Lebesgue spaces on unbounded quasimetric measure spaces, Math. Scand., 116(1) (2015), 5–22. https://doi.org/10.7146/math.scand.a-20448
- Cruz-Uribe, D., Fiorenza, A., Neugebauer, C., The maximal function on variable $L^{p}$ spaces, Ann. Acad. Sci. Fenn. Math., 28 (2003), 223–238.
- Cruz-Uribe, D., Fiorenza, A., Martell, J., Perez, C., The boundedness of classical operators on variable $L^{p}$ spaces, Ann. Acad. Sci. Fenn. Math., 31 (2006), 239–264.
- Diening, L., Maximal function on Orlicz-Musielak spaces and generalized Lebesgue space, Bull. Sci. Math., 129(8) (2005), 657–700. https://doi.org/10.1016/j.bulsci.2003.10.003
- Diening, L., Maximal function on generalized Lebesgue spaces $L^{p(x)}$, Mathematical Ineq. & App., 7(2) (2004), 245–253. dx.doi.org/10.7153/mia-07-27
- Ekincioglu, I., Guliyev, V. S., Kaya, E., Bn−maximal operator and $B_n$−singular integral operators on variable exponent Lebesgue spaces, Mathematica Slovaca, 70(4) (2020), 893– 902. https://doi.org/10.1515/ms-2017-0401
- Ekincioglu, I., Shishkina, E. L., Kaya, E., On the boundedness of the generalized translation operator on variable exponent Lebesgue spaces, Acta Applicandae Mathematicae, 173 (2021), 1–14. https://doi.org/10.1007/s10440-021-00411-8
- Guliev, V. S., On maximal function and fractional integral, associated with the Bessel differential operator, Math. Inequal. Appl., 6(2) (2003), 317–330. dx.doi.org/10.7153/mia-06-30
- Gürbüz, F., Degisken üstlü Lebesgue uzaylarında kaba ¸cekirdekli kesirli maksimal ve integral operatorlerinin genellestirilmis komutatorleri icin bazı tahminler icin Muhendislik, Matematik ve Doga Bilimlerinde Yenilikci Yaklaşımlar, Ekin Yayınevi, T¨urkiye, 2019, 1–11.
- Gürbüz, F., Ding, S., Han, H., Long, P., Characterizations of Rough Fractional-Type Integral Operators on Variable Exponent Vanishing Morrey-Type Spaces, in Topics in Contemporary Mathematical Analysis and Applications, CRC Press, 2020. 10.1201/9781003081197-4
- Gürbüz, F., Ding, S., Han, H., Long, P., Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators, Int. J. Nonlinear Sci. Numer. Simul., 22(6) (2021), 721–739. https://doi.org/10.1515/ijnsns-2019-0180
- Kaya, E., A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces, Open Mathematics, 19(1) (2021), 306–315. https://doi.org/10.1515/math-2021-0041
- Klyuchantsev, M. I., On singular integrals generated by the generalized shift operator I, Sibirsk. Math. Zh., 11(4) (1970), 810–821. http://mi.mathnet.ru/eng/smj/v11/i4/p810
- Levitan, B. M., Bessel function expansions in series and Fourier integrals, Uspekhi Mat. Nauk, 6:2(42) (1951), 102–143. http://mi.mathnet.ru/eng/umn/v6/i2/p102
- Sarfraz, N., Jarad, F., Estimates for a rough fractional integral operator and its commutators on p−adic central Morrey spaces, Fractal Fract., 6(2) (2022), 117. https://doi.org/10.3390/fractalfract6020117
- Sarfraz, N., Aslam, M., Jarad, F., Boundedness for commutators of rough p−adic Hardy operator on p−adic central Morrey spaces, J. Funct. Spaces, 2021 (2021), 1–5. https://doi.org/10.1155/2021/4886197
Year 2022,
Volume: 71 Issue: 3, 710 - 719, 30.09.2022
Abstract
By using the Lp(⋅)−Lp(⋅)−boundedness of a maximal operator defined on homogeneous space, it has been shown that the B−B−maximal operator is bounded. In the present paper, we aim to bring a different approach to the boundedness of the B−B−maximal operator generated by generalized translation operator under a continuity assumption on p(⋅)p(⋅). It is noteworthy to mention that our assumption is weaker than uniform Hölder continuity.
References
- Adamowicz, T., Harjulehto, P., Hastö, P., Maximal operator in variable exponent Lebesgue spaces on unbounded quasimetric measure spaces, Math. Scand., 116(1) (2015), 5–22. https://doi.org/10.7146/math.scand.a-20448
- Cruz-Uribe, D., Fiorenza, A., Neugebauer, C., The maximal function on variable $L^{p}$ spaces, Ann. Acad. Sci. Fenn. Math., 28 (2003), 223–238.
- Cruz-Uribe, D., Fiorenza, A., Martell, J., Perez, C., The boundedness of classical operators on variable $L^{p}$ spaces, Ann. Acad. Sci. Fenn. Math., 31 (2006), 239–264.
- Diening, L., Maximal function on Orlicz-Musielak spaces and generalized Lebesgue space, Bull. Sci. Math., 129(8) (2005), 657–700. https://doi.org/10.1016/j.bulsci.2003.10.003
- Diening, L., Maximal function on generalized Lebesgue spaces $L^{p(x)}$, Mathematical Ineq. & App., 7(2) (2004), 245–253. dx.doi.org/10.7153/mia-07-27
- Ekincioglu, I., Guliyev, V. S., Kaya, E., Bn−maximal operator and $B_n$−singular integral operators on variable exponent Lebesgue spaces, Mathematica Slovaca, 70(4) (2020), 893– 902. https://doi.org/10.1515/ms-2017-0401
- Ekincioglu, I., Shishkina, E. L., Kaya, E., On the boundedness of the generalized translation operator on variable exponent Lebesgue spaces, Acta Applicandae Mathematicae, 173 (2021), 1–14. https://doi.org/10.1007/s10440-021-00411-8
- Guliev, V. S., On maximal function and fractional integral, associated with the Bessel differential operator, Math. Inequal. Appl., 6(2) (2003), 317–330. dx.doi.org/10.7153/mia-06-30
- Gürbüz, F., Degisken üstlü Lebesgue uzaylarında kaba ¸cekirdekli kesirli maksimal ve integral operatorlerinin genellestirilmis komutatorleri icin bazı tahminler icin Muhendislik, Matematik ve Doga Bilimlerinde Yenilikci Yaklaşımlar, Ekin Yayınevi, T¨urkiye, 2019, 1–11.
- Gürbüz, F., Ding, S., Han, H., Long, P., Characterizations of Rough Fractional-Type Integral Operators on Variable Exponent Vanishing Morrey-Type Spaces, in Topics in Contemporary Mathematical Analysis and Applications, CRC Press, 2020. 10.1201/9781003081197-4
- Gürbüz, F., Ding, S., Han, H., Long, P., Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators, Int. J. Nonlinear Sci. Numer. Simul., 22(6) (2021), 721–739. https://doi.org/10.1515/ijnsns-2019-0180
- Kaya, E., A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces, Open Mathematics, 19(1) (2021), 306–315. https://doi.org/10.1515/math-2021-0041
- Klyuchantsev, M. I., On singular integrals generated by the generalized shift operator I, Sibirsk. Math. Zh., 11(4) (1970), 810–821. http://mi.mathnet.ru/eng/smj/v11/i4/p810
- Levitan, B. M., Bessel function expansions in series and Fourier integrals, Uspekhi Mat. Nauk, 6:2(42) (1951), 102–143. http://mi.mathnet.ru/eng/umn/v6/i2/p102
- Sarfraz, N., Jarad, F., Estimates for a rough fractional integral operator and its commutators on p−adic central Morrey spaces, Fractal Fract., 6(2) (2022), 117. https://doi.org/10.3390/fractalfract6020117
- Sarfraz, N., Aslam, M., Jarad, F., Boundedness for commutators of rough p−adic Hardy operator on p−adic central Morrey spaces, J. Funct. Spaces, 2021 (2021), 1–5. https://doi.org/10.1155/2021/4886197
There are 16 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | September 30, 2022 |
| Submission Date | December 1, 2021 |
| Acceptance Date | March 12, 2022 |
| Published in Issue | Year 2022 Volume: 71 Issue: 3 |
Cite
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